Using math to write efficient code in any language

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

Inbuilt max and min functions can minimize verbose if statements.

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.

Ethereum is the second-largest cryptocurrency. The Merge, a mid-September event that will convert Ethereum's consensus process from proof-of-work to proof-of-stake if all goes according to plan, will be a game changer.

Why is Ethereum ditching proof-of-work? Because it can. We're talking about a fully functioning, open-source ecosystem with a capacity for evolution that other cryptocurrencies lack, a change that would allow it to scale up its performance from 15 transactions per second to 100,000 as its blockchain is used for more and more things. It would reduce its energy consumption by 99.95%. Vitalik Buterin, the system's founder, would play a less active role due to decentralization, and miners, who validated transactions through proof of work, would be far less important.

Why has this conversion taken so long and been so cautious? Because it involves modifying a core process while it's running to boost its performance. It requires running the new mechanism in test chains on an ever-increasing scale, assessing participant reactions, and checking for issues or restrictions. The last big test was in early June and was successful. All that's left is to converge the mechanism with the Ethereum blockchain to conclude the switch.

What's stopping Bitcoin, the leader in market capitalization and the cryptocurrency that began blockchain's appeal, from doing the same? Satoshi Nakamoto, whoever he or she is, departed from public life long ago, therefore there's no community leadership. Changing it takes a level of consensus that is impossible to achieve without strong leadership, which is why Bitcoin's evolution has been sluggish and conservative, with few modifications.

Secondly, The Merge will balance the consensus mechanism (proof-of-work or proof-of-stake) and the system decentralization or centralization. Proof-of-work prevents double-spending, thus validators must buy hardware. The system works, but it requires a lot of electricity and, as it scales up, tends to re-centralize as validators acquire more hardware and the entire network activity gets focused in a few nodes. Larger operations save more money, which increases profitability and market share. This evolution runs opposed to the concept of decentralization, and some anticipate that any system that uses proof of work as a consensus mechanism will evolve towards centralization, with fewer large firms able to invest in efficient network nodes.

Yet radical bitcoin enthusiasts share an opposite argument. In proof-of-stake, transaction validators put their funds at stake to attest that transactions are valid. The algorithm chooses who validates each transaction, giving more possibilities to nodes that put more coins at stake, which could open the door to centralization and government control.

In both cases, we're talking about long-term changes, but Bitcoin's proof-of-work has been evolving longer and seems to confirm those fears, while proof-of-stake is only employed in coins with a minuscule volume compared to Ethereum and has no predictive value.

As of mid-September, we will have two significant cryptocurrencies, each with a different consensus mechanisms and equally different characteristics: one is intrinsically conservative and used only for economic transactions, while the other has been evolving in open source mode, and can be used for other types of assets, smart contracts, or decentralized finance systems. Some even see it as the foundation of Web3.

Many things could change before September 15, but The Merge is likely to be a turning point. We'll have to follow this closely.

The web adds millions or billions of pages per day.

How much Google traffic does this content get?

In 2017, we studied 2 million randomly-published pages to answer this question. Only 5.7% of them ranked in Google's top 10 search results within a year of being published.

94.3 percent of roughly two million pages got no Google traffic.

Two million pages is a small sample compared to the entire web. We did another study.

We analyzed over a billion pages to see how many get organic search traffic and why.

How many pages get search traffic?

90% of pages in our index get no Google traffic, and 5.2% get ten visits or less.

90% of google pages get no organic traffic

How can you join the minority that gets Google organic search traffic?

There are hundreds of SEO problems that can hurt your Google rankings. If we only consider common scenarios, there are only four.

Reason #1: No backlinks

I hate to repeat what most SEO articles say, but it's true:

Backlinks boost Google rankings.

Google's "top 3 ranking factors" include them.

Why don't we divide our studied pages by the number of referring domains?

66.31 percent of pages have no backlinks, and 26.29 percent have three or fewer.

Did you notice the trend already?

Most pages lack search traffic and backlinks.

But are these the same pages?

Let's compare monthly organic search traffic to backlinks from unique websites (referring domains):

More backlinks equals more Google organic traffic.

Referring domains and keyword rankings are correlated.

It's important to note that correlation does not imply causation, and none of these graphs prove backlinks boost Google rankings. Most SEO professionals agree that it's nearly impossible to rank on the first page without backlinks.

You'll need high-quality backlinks to rank in Google and get search traffic. 

Is organic traffic possible without links?

Here are the numbers:

Four million pages get organic search traffic without backlinks. Only one in 20 pages without backlinks has traffic, which is 5% of our sample.

Most get 300 or fewer organic visits per month.

What happens if we exclude high-Domain-Rating pages?

The numbers worsen. Less than 4% of our sample (1.4 million pages) receive organic traffic. Only 320,000 get over 300 monthly organic visits, or 0.1% of our sample.

This suggests high-authority pages without backlinks are more likely to get organic traffic than low-authority pages.

Internal links likely pass PageRank to new pages.

Two other reasons:

1. Our crawler's blocked. Most shady SEOs block backlinks from us. This prevents competitors from seeing (and reporting) PBNs.

2. They choose low-competition subjects. Low-volume queries are less competitive, requiring fewer backlinks to rank.

If the idea of getting search traffic without building backlinks excites you, learn about Keyword Difficulty and how to find keywords/topics with decent traffic potential and low competition.

Reason #2: The page has no long-term traffic potential.

Some pages with many backlinks get no Google traffic.

Why? I filtered Content Explorer for pages with no organic search traffic and divided them into four buckets by linking domains.

Almost 70k pages have backlinks from over 200 domains, but no search traffic.

By manually reviewing these (and other) pages, I noticed two general trends that explain why they get no traffic:

1. They overdid "shady link building" and got penalized by Google;

2. They're not targeting a Google-searched topic.

I won't elaborate on point one because I hope you don't engage in "shady link building"

#2 is self-explanatory:

If nobody searches for what you write, you won't get search traffic.

Consider one of our blog posts' metrics:

No organic traffic despite 337 backlinks from 132 sites.

The page is about "organic traffic research," which nobody searches for.

News articles often have this. They get many links from around the web but little Google traffic.

People can't search for things they don't know about, and most don't care about old events and don't search for them.

Note:

Some news articles rank in the "Top stories" block for relevant, high-volume search queries, generating short-term organic search traffic.

The Guardian's top "Donald Trump" story:

Ahrefs caught on quickly:

"Donald Trump" gets 5.6M monthly searches, so this page got a lot of "Top stories" traffic.

I bet traffic has dropped if you check now.

One of the quickest and most effective SEO wins is:

1. Find your website's pages with the most referring domains;

2. Do keyword research to re-optimize them for relevant topics with good search traffic potential.

Bryan Harris shared this "quick SEO win" during a course interview:

He suggested using Ahrefs' Site Explorer's "Best by links" report to find your site's most-linked pages and analyzing their search traffic. This finds pages with lots of links but little organic search traffic.

We see:

The guide has 67 backlinks but no organic traffic.

We could fix this by re-optimizing the page for "SERP"

A similar guide with 26 backlinks gets 3,400 monthly organic visits, so we should easily increase our traffic.

Don't do this with all low-traffic pages with backlinks. Choose your battles wisely; some pages shouldn't be ranked.

Reason #3: Search intent isn't met

Google returns the most relevant search results.

That's why blog posts with recommendations rank highest for "best yoga mat."

Google knows that most searchers aren't buying.

It's also why this yoga mats page doesn't rank, despite having seven times more backlinks than the top 10 pages:

The page ranks for thousands of other keywords and gets tens of thousands of monthly organic visits. Not being the "best yoga mat" isn't a big deal.

If you have pages with lots of backlinks but no organic traffic, re-optimizing them for search intent can be a quick SEO win.

It was originally a boring landing page describing our product's benefits and offering a 7-day trial.

We realized the problem after analyzing search intent.

People wanted a free tool, not a landing page.

In September 2018, we published a free tool at the same URL. Organic traffic and rankings skyrocketed.

Reason #4: Unindexed page

Google can’t rank pages that aren’t indexed.

If you think this is the case, search Google for site:[url]. You should see at least one result; otherwise, it’s not indexed.

A rogue noindex meta tag is usually to blame. This tells search engines not to index a URL.

Rogue canonicals, redirects, and robots.txt blocks prevent indexing.

Check the "Excluded" tab in Google Search Console's "Coverage" report to see excluded pages.

Google doesn't index broken pages, even with backlinks.

Surprisingly common.

In Ahrefs' Site Explorer, the Best by Links report for a popular content marketing blog shows many broken pages.

One dead page has 131 backlinks:

According to the URL, the page defined content marketing. —a keyword with a monthly search volume of 5,900 in the US.

Luckily, another page ranks for this keyword. Not a huge loss.

At least redirect the dead page's backlinks to a working page on the same topic. This may increase long-tail keyword traffic.

This post is a summary. See the original post here

Could this happen?

Medium isn't like other social media giants. It wasn't a dot-com startup that became a multi-trillion-dollar social media firm. It launched in 2012 but didn't gain popularity until later. Now, it's one of the largest sites by web traffic, but it's still little compared to most. Most of Medium's traffic is external, but they don't run advertisements, so it's all about memberships.

Medium isn't profitable, but they don't disclose how terrible the problem is. Most of the $163 million they raised has been spent or used for acquisitions. If the money turns off, Medium can't stop paying its writers since the site dies. Writers must be paid, but they can't substantially slash payment without hurting the platform. The existing model needs scale to be viable and has a low ceiling. Facebook and other free social media platforms are struggling to retain users. Here, you must pay to appreciate it, and it's bad for writers AND readers. If I had the same Medium stats on YouTube, I'd make thousands of dollars a month.

Then what? Medium has tried to monetize by offering writers a cut of new members, but that's unsustainable. People-based growth is limited. Imagine recruiting non-Facebook users and getting them to pay to join. Some may, but I'd rather write.

Alternatives:

• Donation buttons

• Tiered subscriptions ($5, $10, $25, etc.)

• Expanding content

and these may be short-term fixes, but they're not as profitable as allowing ads. Advertisements can pay several dollars per click and cents every view. If you get 40,000 views a month like me, that's several thousand instead of a few hundred. Also, Medium would have enough money to split ad revenue with writers, who would make more. I'm among the top 6% of Medium writers. Only 6% of Medium writers make more than $100, and I made $500 with 35,000 views last month. Compared to YouTube, the top 1% of Medium authors make a lot. Mr. Beast and PewDiePie make MILLIONS a month, yet top Medium writers make tens of thousands. Sure, paying 3 or 4 people a few grand, or perhaps tens of thousands, will keep them around. What if great authors leveraged their following to go huge on YouTube and abandoned Medium? If people use Medium to get successful on other platforms, Medium will be continuously cycling through authors and paying them to stay.

Ads might make writing on Medium more profitable than making videos on YouTube because they could preserve the present freemium model and pay users based on internal views. The $5 might be ad-free.

Consider: Would you accept Medium ads? A $5 ad-free version + pay-as-you-go, etc. What are your thoughts on this?

Original post available here

https://tomconnor.me/wp-content/uploads/2021/08/10x-Engineer-Mental-Models.pdf

I keep returning to the same mental models and tricks after writing and reading about a wide range of topics.

Top 12 mental models

12.

Survival bias - We perceive the surviving population as remarkable, yet they may have gotten there through sheer grit.

Survivorship bias affects us in many situations. Our retirement fund; the unicorn business; the winning team. We often study and imitate the last one standing. This can lead to genuine insights and performance improvements, but it can also lead us astray because the leader may just be lucky.

11.

The Helsinki Bus Theory - How to persevere Buss up!

Always display new work, and always be compared to others. Why? Easy. Keep riding. Stay on the fucking bus.

10.

Until it sticks… Turning up every day… — Artists teach engineers plenty. Quality work over a career comes from showing up every day and starting.

9.

WRAP decision making process (Heath Brothers)

Decision-making WRAP Model:

W — Widen your Options

R — Reality test your assumptions

A — Attain Distance

P — Prepare to be wrong or Right

8.

Systems for knowledge worker excellence - Todd Henry and Cal Newport write about techniques knowledge workers can employ to build a creative rhythm and do better work.

Todd Henry's FRESH framework:

1. Focus: Keep the start in mind as you wrap up.

2. Relationships: close a loop that's open.

3. Pruning is an energy.

4. Set aside time to be inspired by stimuli.

5. Hours: Spend time thinking.

7.

Black Box Thinking…..

BBT is learning from mistakes. Science has transformed the world because it constantly updates its theories in light of failures. Complexity guarantees failure. Do we learn or self-justify?

6.

The OODA Loop - Competitive advantage

O: Observe: collect the data. Figure out exactly where you are, what’s happening.

O: Orient: analyze/synthesize the data to form an accurate picture.

D: Decide: select an action from possible options

A: Action: execute the action, and return to step (1)

Boyd's approach indicates that speed and agility are about information processing, not physical reactions. They form feedback loops. More OODA loops improve speed.

5.

Know your Domain 

Leaders who try to impose order in a complex situation fail; those who set the stage, step back, and allow patterns to develop win.

https://vimeo.com/640941172?embedded=true&source=vimeo_logo&owner=11999906

4.

The Three Critical Gaps

• Information Gap - The discrepancy between what we know and what we would like to know

• Gap in Alignment - What individuals actually do as opposed to what we wish them to do

• Effects Gap - the discrepancy between our expectations and the results of our actions

3.

Theory of Constraints — The Goal  - To maximize system production, maximize bottleneck throughput.

• Goldratt creates a five-step procedure:

1. Determine the restriction

2. Improve the restriction.

3. Everything else should be based on the limitation.

4. Increase the restriction

5. Go back to step 1 Avoid letting inertia become a limitation.

Any non-constraint improvement is an illusion.

2.

Serendipity and the Adjacent Possible - Why do several amazing ideas emerge at once? How can you foster serendipity in your work?

You need specialized abilities to reach to the edge of possibilities, where you can pursue exciting tasks that will change the world. Few people do it since it takes a lot of hard work. You'll stand out if you do.

Most people simply lack the comfort with discomfort required to tackle really hard things. At some point, in other words, there’s no way getting around the necessity to clear your calendar, shut down your phone, and spend several hard days trying to make sense of the damn proof.

1.

Boundaries of failure - Rasmussen's accident model.

Rasmussen modeled this. It has economic, workload, and performance boundaries.

The economic boundary is a company's profit zone. If the lights are on, you're within the economic boundaries, but there's pressure to cut costs and do more.

Performance limit reflects system capacity. Taking shortcuts is a human desire to minimize work. This is often necessary to survive because there's always more labor.

Both push operating points toward acceptable performance. Personal or process safety, or equipment performance.

If you exceed acceptable performance, you'll push back, typically forcefully.